Zoë Wanamaker is no stranger to playing sorely tried wives. Her populous gallery of women in this fix includes, at one end of the social scale, a gutturally Germanic and frizzy-wigged Princess Caroline of Brunswick whose fate – as the arranged spouse of Simon Russell Beale's future George IV (himself already secretly married) – was seen to foreshadow that of Princess Diana in Battle Royal at the National Theatre in 1999.

Wanamaker flooded the stage with the betrayed woman's comically oddball, strongly poignant presence just as, over in suburbia in Terry Johnson's Dead Funny (1994), she projected a scathingly mordant end-of-her-tether wit as a woman who discovers that it is no joke to be 41, desperate for a baby, and married to a humourless comedy buff.

Now, in David Leveaux's revival of Peter Nichols' bruisingly frank Passion Play (1981), which is running at the Duke of York's Theatre, there's a twist to the presentation of the heroine that poses a fresh technical challenge for the actress. Her character, Eleanor, is a music teacher and keen choral singer who has been equably married with children for 25 years to art restorer James (played here by Owen Teale).

When the latter embarks on an affair with a sexy young photographer, it would be case of so far, so conventional, if it weren't for the fact that the new tragicomic duplicity and dividedness within the marriage are signalled by a graphic device. James and Eleanor sprout alter egos, Jim and Nell (Oliver Cotton and Samantha Bond); this transforms the eternal triangle into a pentagon – to decidedly Cubist effect.

I meet Wanamaker at her hotel in Brighton where the production is having a pre-London run. Because of transport problems, I was 40 minutes late but she wafts away my gabbled apologies: "I used the time to have a nice, healthy jog on the beach." She was born in 1949 but looks a good decade younger. Her face (familiar to a wider public through the Harry Potter films and the BBC sitcom My Family) has been likened to that of a sad Pierrot but, offstage, the ironic twinkle, curvy grin and rascally laugh are in constant mutiny against that impression.

Earlier that week, Shakespeare's Globe had announced the opening seasons of its new indoor Jacobean-style Sam Wanamaker Playhouse, named after her visionary actor-father who, when she was three, was forced to flee his native US because of the McCarthyite witch-hunts, and later became the definitive driving force behind the Globe's re-creation. She's been known to say that he would not like the idea of a theatre in his name.

"I think it was because when he was looking for funding of the Globe, so many people said, 'Well, you can have some money, if you will name a pillar after me', and so on. And he got really tired of that." She agrees, though, that in age when it's become routine for entire venues to be rechristened on the grounds of finance (the Royal Court Jerwood Theatre, say, the great man (who died in 1993) might find the thought of the Sam Wanamaker Playhouse easier to bear.

"Dad would talk to anyone in the street and take taxi drivers into the Globe site to show them what was going on." As a father and fellow-professional, "the first Method actor in this country", though, he could occasionally be "quite scary". She has said in the past that he would give her notes on her performances. I asked whether she would like to share an example and, after a little hesitation, she replied with an instance that shows how bracing and daunting it must have been to build a career under so sharp a gaze.

In 1986, she was in Wrecked Eggs, part of a David Hare double bill at the National – "very, very well directed" by the author. "Dad said, 'That's the worst performance I have ever seen you give. You are acting listening but you aren't really listening." What he'd realised is that I was trying to get Irene Worth to do what she had done in rehearsals and that I was too busy attempting to re-create that to do my job properly – which was to concentrate on what she was now giving me. It was a painful thing to hear from him." And ironic, in the long run, because as we will see in relation to Passion Play, the psychological texture she gives to art of listening onstage is one of Zoë Wanamaker's many great strengths as a theatre artist.

Our encounter takes place the lunchtime after the press opening of the new Adrian Lester/Rory Kinnear Othello at the National and she is keen to hear how it had gone. This leads to talk of her own groundbreaking portrayal of Emilia, wife of Iago, in Trevor Nunn's celebrated 1989 chamber production set during the American Civil War.

Her Emilia smoked a pipe – historically "the soldiers were given a ration of cannabis and Emilia had contrived to get some" – and she was evidently in an abusive and sex-starved marriage to Ian McKellen's buttoned-up Iago who was, revealingly, a tidiness freak ("He got tidier and tidier through the run," laughs Wanamaker). "I did a lot of research into women who are in denial about relationships that have gone terribly wrong – even the wives of convicted murderers – and who delude themselves that one day it will get better."

It's this close naturalist exploration of the hinterland that gives her characterisations their depth and density. She points out that when she played Beatrice to Simon Russell Beale's Benedick, in Nick Hytner's NT production of Much Ado About Nothing, they decided that the witty, self-protective sparring between the characters was the result of "unfinished business. So we imagined a whole back-story in which they had already had a secret physical affair that had gone wrong. Perhaps she had risked too much and one day he did a runner. Simon and I then went away and thought up other details that we deliberately tell each other" so that their versions of the past would realistically be contested and rivalrous.

Wanamaker says that she understands, from personal experience, how this line on Beatrice "encapsulates the experience of a lot of women of our own era who don't feel that they have to get hitched and yet because they are deeply romantic think that a marriage has to be perfect". She always reckoned that she would be a singleton for life – "but then I got lucky" – and, at the age of 45, she married the distinguished actor (and dramatist) Gawn Grainger.

Hytner praises Wanamaker's earthiness: "Zoë and Simon are in many ways very different as people. But they are both beer-and-cigarettes. They can do 'airy' because they are so earthy." David Leveaux, who last directed her in his 1997 Donmar Warehouse production of Sophocles' Electra (which won her an Olivier Award) wanted to constellate Passion Play around her from the outset. "I sent her the script a couple of years ago and she called me and said, 'This is going to take brutal honesty. I'm in.'" He describes her as "a complete modern" (even in classical texts) in the sense that "with her ability to pack an awful lot of melody into a very little tune", she works in short, disarmingly immediate units. And this is perfect for "Nichols' black diamond of a sex comedy".

The relationship between the characters and their alter egos is, Leveaux explains, never a simple question of official self and inner voice but shifts, richly and messily, through mentoring, collusion, antagonism et al. Because the quartet very often have overlapping, "simultaneous" conversations, this means that the characters very often have to keep their response to what has just been said to them suspended until the other couple have finished". How aware are they of the entire conversation? "Luckily, Zoë is supreme at living in the moment. Every beat of her suspended silences in those scenes is a mosaic-like piece of complex subtext." Sam Wanamaker's note about Wrecked Eggs seems to have been taken to heart.

Applauding her dark "inner clown", Leveaux says that, in her luminous emotional candour, she is, for him, "like a walking Rothko". It's an initially startling analogy that soon makes a lot of sense – even if, as Passion Play will doubtless remind us, Wanamaker's colours are rather more resistant to fading.